Communication data in the communication network of the islanded micro-grid can be disturbed in many ways, such as data attack or packet loss. To improve the control effect on the voltages and frequencies obtained by droop control of distributed energy resources (DERs) facing communication data disturbance (CDD), a response hierarchical control strategy is proposed in this study. Based on the concept of the cyber physical system, the control structure is divided into two layers: the cyber layer and physical layer. In the cyber layer, firstly, the effect of the CDD on the micro-grid system is analysed and then, an event-triggered data compensation method combining the back-propagation neural network and extreme learning machine is proposed in this layer to solve the problem of the CDD. In the physical layer, firstly, the droop control is used as the primary control to control the voltages and frequencies of DERs and then, a novel virtual leader-following consensus control method considering time-delay is proposed in this layer. Also, it is used to complete the secondary control of the voltage and frequency obtained by primary control. In the end, the simulation results confirm the effectiveness of the proposed hierarchical control strategy under CDD.